Consecutive Integers Calculator
MathFind n consecutive integers that add up to a given sum.
Smallest Integer
The smallest of the n consecutive integers, x = (S - n(n-1)/2) / n.
Largest Integer
15.0000
The largest of the n consecutive integers.
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Creators
Odeh Ahwal0people find this calculator helpful
Views
Helpful
Saved
Embeds
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Frequently Asked Questions
How is the formula for consecutive integers derived?
If x is the smallest of n consecutive integers, they are x, x+1, x+2, ..., up to x+(n-1). Adding them all together gives n*x plus the sum 0+1+2+...+(n-1), which equals n(n-1)/2. Setting this equal to the target sum S and solving for x gives x = (S - n(n-1)/2) / n.
What if the result is not a whole number?
That means no set of n consecutive whole integers adds up to exactly that sum. For example, no two consecutive integers can sum to an odd number, since one is always even and one odd, so the smallest-integer result would come out as a non-integer.
Does this work for consecutive even or odd integers too?
Not directly, this calculator solves for plain consecutive integers stepping by 1. Consecutive even or odd integers step by 2 instead, which changes the underlying formula.
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